Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26011868 | C2 | semidirect |
| 2. #26011686 | C2 | semidirect |
| 3. #26011244 | C2 | semidirect |
| 4. #26011234 | C2 | semidirect |
| 5. C8×D4×C173 | C2 | semidirect |
| 42. D4×C173 | D8 | semidirect |
| 51. C8×C173 | D8 | semidirect |
| 70. C173 | #1667 | semidirect |
| 74. C8×D4 | D173 | semidirect |
| 112. D4 | D1384 | semidirect |
| 122. C8 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011868 | 2 |
| #26011686 | 2 |
| #26011244 | 2 |
| #26011234 | 2 |
| C8×D4×C173 | 2 |
| #1667 | 173 |